Unit Review: Conic Sections

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Objective

SWBAT review the important concepts of this unit.

Big Idea

Summarize the big ideas of this unit.

Lesson Author

Tim Marley

Troy, MI

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Precalculus and Calculus

Standards

HSG-GPE.A.2

Derive the equation of a parabola given a focus and directrix.

HSG-GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

HSG-GMD.B.4

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

Check Homework

10 minutes

Yesterday my students had a homework assignment from their textbook where they had to graph a couple conic sections that had been rotated. One of them was particularly tedious (3x^2 - 2sqrt(3)xy +y^2 +2x +2sqrt(3)y = 0, so there are usually lots of questions about it. I will have a student who got the correct answer present their work on the document camera.

One thing I tell students is that the xy-term should always go away when we convert it to a new equation in the x'y'-plane. That is the whole point of this process - to make the equation into a form we are familiar with so that we can graph like the conics that are horizontal or vertical.

Unit Review

40 minutes

Here is the unit review that I give my students and have them work on for the rest of the hour. They are in their table groups and so they can talk through their thoughts while working.

In this video I discuss some of the problems on the worksheet.

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